© Christopher Gregory for The New York Times Fernandez Juncos Avenue in San Juan, Puerto Rico. The government is in a position to run out of money as early as December.

Known until this month as the Trump International Golf Club Puerto Rico, it was built as a for-profit venture, subsidized by federal taxpayers and backed by the island’s powerful Government Development Bank, which sold to investors and guaranteed repayment of more than $50 million in tax-exempt bonds.

Despite the Trump name, which the former owners licensed from the billionaire investor and now presidential candidate Donald J. Trump, the resort failed to attract enough wealthy golfers since the first tee-off in 2004.

This year, it went bankrupt. (Mr. Trump was not involved in the financing or operation of the club.) Then, about a week ago, a buyer scooped up the property, wine cellar and all, for a mere $2.2 million and is rushing to get it ready for a Professional Golfers Association tournament in March, a nationally televised event and a point of pride for Puerto Rico.

The name “Trump” is being removed from the signs, to be replaced by “Coco Beach.” A spokesman for the buyer said it was committed “to making this a showcase for the island and the community.”

But the new owner, OHorizons Global, a private investment firm based in San Juan, did not take over the existing debt. The Government Development Bank is still making payments on the bonds that are outstanding; the last one is due in 2034. The firm declined to speak on the record about the purchase and its plans.

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The deal and how it came to be provide telling insight into the workings of the Government Development Bank, which is responsible for managing the $72 billion in debt that the island has amassed — and says it cannot hope to repay. Although it has so far defaulted on only a tiny portion of the debt, the next test comes on Tuesday, when the bank is scheduled to make a $354 million bond payment. It will not yet say whether it can or should meet the deadline.

Even if it does, however, it faces a series of legal and tactical challenges through December, with another major test on Jan. 1.

Deals like the golf resort are not the only reason the Government Development Bank has found itself at the center of Puerto Rico’s financial jam. But it is an example of how the bank helped borrow on behalf of public and private enterprises over the years, then ended up with much of the debt, even when deals failed to fulfill their original purpose: the development of Puerto Rico.

“Guarantees are good when you have a good venture,” said Melba Acosta Febo, the president and chairwoman of the bank. A lawyer and Harvard-trained accountant, Ms. Acosta is also now serving as a kind of financial magician, making cash appear as needed and staving off most defaults, at least for now.

In an interview in New York last week, Ms. Acosta acknowledged that even she found the “debt stack” confusing and called the golf venture “a great example” of how things had gone wrong.

“But this is just one example,” she added. “We have many failed ventures that have not been able to pay their debts.”

It is not clear how long her particular brand of magic can continue. Puerto Rico has been warning that it is running out of cash, and Ms. Acosta said the “extraordinary measures” she had been using to produce cash so far were unsustainable. The measures include delaying people’s tax refunds, borrowing from the island’s workers’ compensation fund, forcing community credit unions to hand over their cash in exchange for i.o.u.s, and now, even considering whether the island should withhold millions of dollars in holiday bonuses to government workers and retirees.

The bonuses are paid just in time for Christmas shopping. But the benefit is not only to consumers. The sales tax revenue from the year-end rush to spend help fill the government’s coffers, and some are dedicated to making bond payments. “Usually we get that back,” Ms. Acosta said, explaining how a government outlay of more than $120 million in bonuses could be justified, even during a financial crisis.

The bond payments due on Tuesday are for principal and interest on debt issued by the development bank, but guaranteed as a general obligation by the island’s government. That puts them near the top of Puerto Rico’s hierarchy of credits.

People briefed on the situation say that Gov. Alejandro García Padilla, who must make the final decision, has revealed almost nothing about his intentions. He traveled to Europe last week, in part to court investors there and in part, these people say, to put some space between himself and the cacophony of advice flowing his way.

“The decision matrix is like choosing whether you want to die by cyanide or by hanging,” said one person with knowledge of the governor’s dilemma, who spoke on the condition of anonymity. “I’ve never seen anything as complicated as this.”

Some advisers are said to be urging the governor to play by the rules, make the payment on Tuesday and build good will in Congress, which holds the keys to what could be Puerto Rico’s ultimate salvation: access to bankruptcy courts. As a United States territory, it cannot legally take shelter from its creditors in bankruptcy; the law explicitly excludes it.

Yet many officials on and off the island believe meaningful debt relief is possible only in bankruptcy and have been calling on Congress to amend the law and give access to at least part of the island’s government.

On Tuesday, Senator Charles E. Grassley, the Republican chairman of the Senate Judiciary Committee, will hold a hearing on the bankruptcy question, the latest in a series of hearings intended to consider help for Puerto Rico.

But other advisers to the island’s government have been urging the governor to default on the debt, saying that only a catastrophe would move Congress — especially Republians — to help. “We need Chapter 9,” said Ms. Acosta, referring to the bankruptcy chapter used by cities and other local governments. “Give us the tool and we will finalize what we are doing.”

Ms. Acosta said the enormous financial quagmire facing the bank was inextricably tied to its history as a unique institution on United States-controlled soil.

The bank was founded in 1942 by Rexford G. Tugwell, who was appointed governor of the commonwealth by President Franklin D. Roosevelt. (Puerto Ricans have elected their own governors since 1948.) Its mandate was to foster development, primarily by financing electricity at a time when the island was known as “the Poorhouse of the Caribbean,” with an economy based almost entirely on sugar cane.

But after an unrelated financial scandal three years later, the bank was given tremendous new powers: to advise the government on transactions, to vet and restructure bond deals, to hold public money in trust, to borrow money for other government agencies, to lend its own money to those agencies, to finance private enterprise, and any number of other powers meant to ensure that the island was not cheated by commercial banks on the mainland.

“You’re really not going to find any similar entity in any state,” Ms. Acosta said.

States typically decentralize their financial activities. But even today, Puerto Rico tends to run everything through the Government Development Bank. Its job is “really a combination of things that the Treasury, the New York Fed and a development bank like the Inter-American Development Bank do,” she said.

In its early years the bank helped engineer an economic boom, financing low-cost housing for soldiers returning from World War II, then school construction for their children. It even financed the restoration of historic Old San Juan and took on projects like shopping centers and manufacturing plants, which private lenders still considered too risky.

Puerto Rico’s per capita income doubled from 1950 to 1960. And after Fidel Castro’s revolutionaries took control of Cuba in 1959, Washington put Puerto Rico on a pedestal, extending minimum wage laws to the island and tax breaks to corporations willing to set up shop there, and parading its “Showcase of Democracy” before the world.

But even after the growth cooled, the borrowing continued.

“The problems started when the Government Development Bank started lending for deficit financing instead of capital improvements,” Ms. Acosta said, “and when it started lending to entities that didn’t have a source of repayment.” In theory, it was illegal for the development bank to grant loans to borrowers that had no way to pay them back.

“The law didn’t include the public corporations,” she said, referring to the big, free-standing government enterprises that provide crucial services like electricity, drinking water and road maintenance. “That loophole explains the amount of the loans that were given.”

Ms. Acosta recalled that when she became Puerto Rico’s budget director, in 2001, she was horrified to discover $4 billion of loans from the development bank to various government agencies on the island.

“We were like, ‘$4 billion! Oh, my God!’ And we went out to the market and we started to repay it,” she said.

But when she returned to government as the Treasury secretary in 2012, the bank’s loans had grown to $10 billion.

Some of the loans were to companies; others were to local governments on the island that could no longer borrow on their own. The capital markets were still happy to do business with the Government Development Bank, not just because of its high level of sophistication, but also because it could structure bond deals that were remarkably easy to sell. Not only was there that constitutional guarantee, but Puerto Rico’s legal status as a territory allows it to pay interest that is exempt from federal, state and local taxes to investors in all 50 states.

Today, given its financial straits, Puerto Rico could not borrow to make the coming bond payments even if it wanted to. It may have to get the cash by raiding government programs.

At the new Coco Beach golf course in Rio Grande, meanwhile, grass is being planted, fresh sand spread in the sand traps and updated appointments installed in the clubhouse. The new owners expect to be ready when CBS turns on its cameras and the world’s top golfers show up to compete for a $3 million purse.